Many chemical reactions are intrinsically coupled with transport phenomena. In realistic systems, both the chemical reactions as well as the transport phenomena are functions of space. Despite spatial distribution, it is customary to fit transport and kinetic properties in experiments to simplified lumped models. This paper outlines a method to acquire unknown system properties in reacting systems with transport coupling. Rigorous metrics to quantify confidence levels of these distributed models and their parameters to represent the experimental data will also be computed. We will advocate the advantage of deploying confidence information together with apparent physical and chemical properties for flexible process design. Hence, we will find the most cost-effective design subject to the accurate statistical error information of the model parameters. The paper will introduce mathematical foundations and nonlinear programming solutions based on trust region methods with inexact function and gradient evaluations specifically designed for inversion problem of distributed systems. A comprehensive example for the optimal design of catalytic pellet reactor will illustrate the proposed approach.